 | Euclides - 1826 - 226 pages
...continually produced shall meet on that side where the angles are less than two right angles. AXIOMS. 1. Things which are equal to the same are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...because the point B is the * 1-, Deficentre of the circle ACE, BC is equal to BA: but it has nitionbeen proved that CA is equal to AB; therefore CA, CB, are each of them equal to AB: but things which are equal to the same thing are equal* to one another; therefore CA is equal to CB... | |
 | John Martin Frederick Wright - 1827 - 344 pages
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous ?" " Things which are equal to the same, are equal to one another." " Very good, Sir. What the second, and what the third?" "If equals be added to equals the sums are... | |
 | English literature - 1827 - 608 pages
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous V " Things which are equal to the same, are equal to one another." " Very good, Sir. What the second, and what the thirdV " If equals be added to equals, the sums are... | |
 | John Martin F. Wright - 1827 - 632 pages
...But what is the first axiom of Euclid, or of Geometry, as I may say, the terms being synonymous ?" " Things which are equal to the same, are equal to one another." " Very good, Sir. What the second, and what the third?" " If equals be added to equals the sums are... | |
 | George Bentham - Logic - 1827 - 304 pages
...which a syllogistic conclusion can be founded ? Such may, perhaps, be found the four following : 1. Things which are equal to the same, are equal to one another. 2. When of two things, one only is equal to a third, and the other is not equal to that third, these... | |
 | Leeds grammar sch - 1828 - 364 pages
...: but Patience is equal to Poverty ; therefore Patience and Economy are each equal to Poverty ; but things which are equal to the same are equal to one another; therefore Patience and Economy are equal to one another ; wherefore the three, Patience, Economy, and... | |
 | Timothy Walker - Geometry - 1829 - 138 pages
...and are to geometry, what the foundations are to a building. Euclid's axioms are the following : I. Things which are equal to the same are equal to one another. 2k If equals be added to equals the wholes are equal. 3. If equals be taken from equals, the remainders... | |
 | William Sewell - Classical education - 1830 - 390 pages
...experiment. A child never doubts that the fire which burnt him yesterday, will burn him to-day, or that two things which are equal to the same, are equal to one another, where he .has once seen the axiom illustrated by a single example—and hence one great advantage in... | |
 | George Peacock - Algebra - 1830 - 732 pages
...represented, or in terms of which they are expressed: without such a definition, the proposition that " things which are equal to the same are equal to one another," could no longer be considered as axiomatic, inasmuch as we should be at a loss for the principle or... | |
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AB; but things which are equal to the same are equal to one another... 
